Here, \(\hat{\mathbf {a}}_y=h(\mathbf {z}_a)\)  is output from projection classifier \(h\) , which represents the projection of the latent embedding \(\mathbf {z}_a\)  onto the semantic space \(\mathcal {A}\) . Also,
\(\tilde{\mathbf {z}} = \eta \mathbf {z}_{a} +(1-\eta )(\alpha \mathbf {z}_a+\beta \mathbf {z}_v)\)  and \(\tilde{\mathbf {a}}_y = \eta \mathbf {a}_y +(1-\eta )(\alpha \hat{\mathbf {a}}_y+\beta \mathbf {a}_y)\)  with \(\beta =1-\alpha \)  and \(\eta \sim U(0, 1)\) . Additionally, \(\lambda \)  is a weighting coefficient. Note that \(D_{2}\)  is different from the vanilla discriminator \(D_{1}\)  and has a triple adversarial formulation [1]}. Firstly, by incorporating the projection classifier output \(\hat{\mathbf {a}}_y\) , it enables to jointly train the visual encoder \(f\) , semantic encoder \(g\)  and projection classifier \(h\)  while imposing domain-invariance. In addition, we design Eq. REF  to treat \((\mathbf {z}_{a},\mathbf {a}_{y})\)  as real samples and \((\mathbf {z}_{v},\mathbf {a}_{y})\)  , \((\mathbf {z}_{a},\hat{\mathbf {a}}_{y})\)  as fake samples. This acts as a minimizer of the reverse KL divergence i.e., \(KL[(z_{a},a_{y})||(z_{v},a_{y})]\)   [2]} (in contrast to \(D_{1}\)  that minimizes forward KL as described in Sec. REF ) between the visual and semantic spaces. We find that this leads to better generalization by alleviating the mode collapse issue, and thus enables our model to capture multiple modes of the data distribution [2]}. Next, the semantic projector classifier \(h\)  is updated to minimize:
